Fire control systems



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United States Patent G M 3,339,457 FIRE CGNTROL SYSTEMS Lucas Pun, Geneva, Switzerland, assignor to Brevets Aero-Mecanques S.A., Geneva, Switzerland, a society of Switzerland Filed June 21, 1965, Ser. No. 465,394 Claims priority, application Luxembourg, June 26, 1964, 46,404; Aug. is, 1964, 46,787 18 Claims. (Cl. 89-41) ABSTRACT OF THE DISCLOSURE The angular coordinates of a target are determined continuously Whereas the distance thereof is determined at regular time intervals. The angular coordinates of the gun are calculated from said angular coordinates of the target, said distance, the duration of said intervals and the firing tables, the time of Hight of the projectile being calculated by an algorithm, repetitive, but without iteration, from an estimated time of Hight and said duration. The target is preferably followed by a laser rangetinder.

The present invention relates to tire control systems, and in particular to systems of this kind for use with quick tiring antiaircraft light guns. The invention is more especially concerned with systems making use of a discontinuous lasel for measuring the distance of the target.

The chief object of this invention is to provide a system of this kind which is better adapted to meet the requirements of practice in particular concerning the small weight and volume of the system, its facility of use by a small number of gunners, the rapidity of spotting and facility of following the target, the quickness and precision of the determination of the distance between the gun and the target and the reliability of the system.

The system according to the present invention comprises means for determining substantially in a continuous manner the angular coordinates, in particular the bearing (or azimuth) and the site of the target which is followed substantially in a continuous manner. According to a first feature of this invention this system comprises, on the one hand, means for measuring at successive moment separated by constant intervals the distance of the target from the gun advantageously by means of a laser rangelinder working by impulses with a repetition period shorter than one second and supplying digital indications, and, on the other hand, means for determining the angular coordinates, and in particular the vertical and horizontal angular coordinates, of the gun barrel, so that a projectile Hred therefrom normally strikes said target, from said angular coordinates of the target determined in a continuous manner, from the distance of the target from the :gun determined at successive moments, from the duration of the time intervals between said successive moments and from firing tables giving essentially, as a function of the distance of the target, the time of Hight of the projectile and the elevation angle to be given to the gun barrel, the calculated time of Hight of the projectile being determined, by an algorithm, repetitive, but without iteration, from an estimated approximate time of Hight ofthe projectile and from the duration of said time intervals.

According to another feature of the invention, in a fire control system comprising a computer determining, from the successive values of the bearing and the site of the target and from the distance of said target from the gun,

the angular coordinates of the gun barrel, there are provided coders delivering the cosine and the sine of the target bearing and site for successive positions of said target, Vgenerator means for delivering the tangent of the 3,339,457 Patented Sept. 5, 1967 elevation angle of the gun at least as a function of the square of the distance of the target, generator means for delivering the duration of the time of flight of the projectile at least as a function of the square of the distance of the target, computer units determining, from the respective values that have been delivered, the tangents of the angular coordinates to be given to the gun, and means for placing the gun barrel under control of said computer units, the computer being essentially of the digital type and comprising digital units which receive in the digital form the distance of the target from the gun and the respective values delivered by the coders and the generators means and deliver, also in the digital form, the tangents of the angular coordinates to be given to the gun barrel.

According to a third feature of the present invention, in a system for controlling the firing of a projectile, there are provided means for first determining, from an estimated approximate time of Hight of the projectile, the coordinates of the future point where said target will be located at the end of said estimated approximate time of Hight, for deducing from the Iindications of the firing tables a first calculated approximate time of Hight corresponding to this future point, for subsequently determining, from this first calculated approximate time of Hight, new coordinates of a future point corresponding to this first calculated approximate time of Hight, for deducing from the indications 0f the tiring tables, a second calculated approximate time of Hight and finally for deducin a raw time of Hight by the following formula:

Ts1-2T50iT0 2d wherein Tb is the raw time of Hight, To the estimated approximate time of Hight, Ts@ the rst calculated approximate time of Hight, TS1 the second calculated approximate time of Hight and dt the duration of the time intervals between the successive determinations of the distance of the target from the gun.

According to a fourth feature of the present invention in a Hre control system for a gun firing on a target, there are provided means for determining first an estimated approximate time of Hight of the projectile by dividing by a predetermined number the present distance of the target from the gun, and means for immediately giving the gun barrel the tiring coordinates determined from this approximate time of Hight.

According to a :lifth feature of the present invention, there is provided, in a fire control system for a gun tiring on a target, a laser rangender, comprising at most rudimentary cooling means and operated, from the moment the target is first taken into charge, to perform only a small number of measurements, in particular about ten measurements, until there is obtained an accurate determination of the coordinates of the target at a given moment and of the components of its velocity vector, the subsequent positions of the target being determined by calculation, the path of travel of the target being supposed to be rectilinear and the speed of the target being supposed to be constant.

Preferred embodiments of the present invention will be hereinafter described, with reference to the appended drawings, given merely by way of example, and in which:

FIG. l is a diagrammatic perspective view of an antiaircraft gun provided with a lire control system made according to the invention;

FIG. 2 is a block diagram showing the chief units of a iire control system according to the invention making use of the discontinuous distance indications supplied by a pulsed laser;

FIG. 3 diagrammatically shows the path of travel of a target such as an aircraft, the position of the gun of FIG. 1 and of its barrel and the chief angles and distances brought into play in the system of FIG. 2;

FIG. 4 is a block diagram of the tracking computer control units of the gun of FIG. 1;

FIG. 5 shows a control unit of the gun of FIG. l;

FIG. 6 is a block diagram of the computer unit ol FIG. v4;

FIG. 7 is a diagram showing the availability of the values or magnitudes and the switching phases of the computer unit of FIG. `6;

FIG. 8 illustrates a digital embodiment of the unit of FIG. 6;

FIG. 9 shows an abacus or system of curves intended to facilitate the explanation of the application of the repetitive, but without iteration, algorithm brought into play in the computer of FIG. 6 for determining the time of flight of the projectile.

FIG. l is an abacus intended to facilitate explanation of the determination of the correction to be made when determining the time of liight corresponding to the duration, different from zero, of the determination of the angular coordinates of the gun barrel;

FIG. l1 is a block diagram showing a regeneration unit extrapolating the path of the target when the latter ceases to be seen by the gunner;

FIG. l2 shows a modification of the control unit;

FIG. 13 shows a modification of the portions AA of FIG. 6.

FIG. 1 diagrammatically shows a light antiaircraft gun, for instance an automatic gun of 3() mm. caliber, provided with a lire control system according to the invention.

This ligure diagrammatically shows the gun mount 11, which essentially comprises a fixed base 12 and a rotary support 13 rotatable about a vertical axis ZZ.

This rotary support 13 carries the following elements:

(a) A first casing 14 containing the aiming control system which comprises a mechanism including hydraulic motors and pumps which will be hereinafter described in detail with reference to FIG.

(b) A second casing 15 secured to casing 14 and containing an electronic computer, advantageously of the digital type which will be described in detail hereinafter, chiefly with reference to FIGS. 6 and 8;

(c) A laser rangeiinder 16 mounted on a column 17 carried by the second casing 15, in such manner as to be rotatable about horizontal axis y-y and inclined axis z-z, this rangefinder, which will be described with reference to FIG. 2, being for instance of one of the types manufactured by the American firm Hughes Aircraft Company (Culver City, Calif.) under the designation of colidar rangefnder and which includes:

A transmitter 18 of red or infra-red coherent light pulsed signals sent in the direction shown by arrow Em;

A receiver 19 for the coherent light echoes reflected from a target in the direction shown by arrow R;

A telescope 20 for sighting and optical tracking of the target, with an eyepiece 21 where the gunner who is to track the target places his eyes;

Control means 22;

A casing 23 containing a unit for calculating the distance of the target from the gun; and

Means for cooling the laser (not shown);

(d) A system 24 fixed to the rear face 25 of casing 14 through supporting rods 26, said system 24 comprising:

An internal combustion engine 27, such as an internal combustion engine or a diesel engine, supplying power to the whole of the re control system;

A dynamo-electric generator 28 driven by engine 27 and supplying the electric current necessary for the respective electronic units, the cooling means and the means for starting the laser (flash tube 39 and its power feed unit 40 as illustrated by FIG. 2); and

A seat 29 for the gunner who tracks the target through eyepiece 21;

(e) A cradle 30 supporting the barrel 31 of the gun and the feed magazine 32 thereof, cradle 30 being pivotable about a horizontal axis YY; and

(f) A shield 33 and a trigger pedal 34, both carried by casing 14.

FIG. 2 shows the various measurement, computer and control units of the Igun of FIG. l, further illustrating some details concerning the laser rangelinder 16. The laser, which is of the discontinuous operation type, comprises for instance a ruby parallelepipedal crystal or rod 35, constituting the active substance and having a reflecting rear face 36 and a partly transparent front face 37 for transmitting an optical beam 38 every time the active particles of the crystal have been brought to a given energy level by a helical flash tube 39 which surrounds crystal 35 and which is fed with current from a power feed -unit 40 (of approximately 15 volts, 150 watts) brought into action at regular time intervals by a control device 41. It is unnecessary to give further indications concerning the operation and the starting of the ruby laser because they are well known in the art. It should merely be reminded that beam 38 is a beam of monochromatic coherent light (either red or infrared, in particular of 6943 Angstroms) very intensive in its wave length and of very small angle of aperture. This angle is still reduced by an optical collimator system 42. In particular a colidal rangeliuder delivers a beam 38a the angle of aperture of which is of the order of magnitude of one milliradian. A shutter 43, also controlled by device 41, permits of adjusting the moments of transmission of the rangeinder beam 38a in the direction of the arrow Em.

This beam is partly reflected by a target, such as an aircraft, in the same manner as a beam of UHF electromagnetic waves in a radar rangelinding system, and it returns in the form of an echo beam 44 the axis of which is R. The reflected beam 44 is concentrated by mirrors 45-46 and passes through diaphragm 47, provided in mirror 45. A selective filter 48 (which may be replaced by an amplifying laser) permits the passage of the radiations of beam 44 ranging Within a very narrow frequency band the center of which corresponds to the monochromatic frequency of transmission of the ruby crystal 35 (generally 6943 Angstroms) so as to eliminate the parasitic ambient light and to increase the signal to noise ratio. The concentrated and liltered useful light echo 49 is received on the photo-cathode 50 of a photomultiplier tube 51 the output of which, representative of the amount of light received by it, is amplied in an amplifier 52. The output of amplifier 52 is sent to the computer unit 53 of the laser, housed in casing 23 (FIG. l).

This computer unit 53, which is supplied together with the laser by the manufacturer, deduces, in particular in the digital form, the distance d between the target and the laser from the time necessary for coherent light to travel from the laser to the target and back from the target to the laser (to every micro-second of time corresponds a distance of m. between the laser and the target). In the -case of a colidar rangefinder, unit 53 delivers to computer 54 the distance d in the digital form with an approximation of about 10 m., d ranging between 400 and 4500 m. Computer 54, housed in casing 15 (FIG. l), also receives the values of the sighting angles (to wit the bearing g and the site s) from casing 23, carried by column 17 displaced by the gunner. Said gunner, seated on seat 29, looks through telescope 20, to keep the image of the target on the point of intersection of the cross-wires of said telescope, angles g and s representing the spherical coordinates of the yaxis 0f telescope 20.

Computer 54 (started in operation by control device 41) determines, according to the present invention and as it will be hereinafter described, the horizontal G and vertical S angular coordinates of the barrel 31 (FIG. l) of gun 1 so that a projectile fired from said `gun reaches the target. Control system 55, located in casing 14 gives cradle 30 and therefore gun barrel 31 the angular positions, with respect to axes ZZ and YY, corresponding to said angles G and S respectively.

Before describing the improvements according to the present invention the theory of prediction in antiaircraft systems will be shortly reminded with reference to FIG. 3.

FIG. 3 shows, at TA, the path of travel, supposed to be rectilinear, of a target during the period it is tracked by the fire control system supposed to be positioned, together with the antiaircraft gun, at point C. The axis of the gun Ibarrel 31 is shown at c. On this path of travel TA, the target has been `shown in two particular positions thereof, to wit a position A called present position, which is the position of the aircraft when its coordinates are measured by the fire control device, and a position F, called future or set forward position, which is the position of the target when it is struck by a projectile fired from the -gun barrel if prediction and fire control are correct.

The various factors to be taken into account are designated, in FIG. 3 by the following references:

C-gun;

CX-reference line (North-South) in the horizontal plane of gun C;

A-present position of the target;

a-vertical projection of A on the horizontal plane of gun C;

Ka--projection of a on reference line CX;

Xa, Ya, Za-coordinates of the present position A of the target;

g-bearing (or azimuth) of the present position A;

s--site of the present position A;

d-distance from gun C to present Iposition A;

F-future, or set forward, position of the target;

f-vertical projection of F on the horizontal plane of gun C;

K-projection of f on reference line CX;

Xf, Yf, Zf-coordinates of the future position F of the target;

gf-bearing (or azimuth) of the future position F, equal l to the bearing (or azimuth) G of the gun firing a projectile which strikes the target in position F;

sfsite of future position F;

df-dist'ance from gun C to future position F;

h-angle of elevation of gun barrel c;

S-equal to sf-I-h, angle of gun barrel c with the horizontal plane; l y i TA-path of travel of the target;

Ta-projection of TA on the horizontal plane;

dc-distance of gun C-to the path of travel of the target;

vx, vy, vZ-components of the speed v of the target between positions A and F, this speed v being an algebraic value, Ipositive for an aircraft flying away from gun C and negative for an aircraft ying toward said gun.

The following relations exist between these factors:

Yf m gf XF (s) According to the main feature lof the invention:

0n the one hand, the angular coordinates, and in particular the bearing (or azimuth) g and the site s of the target, tracked substantially in a continuous manner (continuity being ensured by extrapolation when the target is 10st of view by the gunner), are determined substantially in a continuous manner and the distance d of the target from the gun, at successive moments t1, t2, t3, etc., such that the period of repetition dt is lower than one second, is determined by -means of a laser rangender, and

On the other hand the angular coordinates, in particular the horizontal angle G and the vertical angle S of gun axis c, that must be given to gun barrel 31 to cause a projectile fired from said gun to 4strike the target are -determined from said angular coordinates g, s, of the target, from said distance d of the target, from said period of repetition dt and from ring tables giving, essentially as a function of the distance of the target from the gun, the time of flight T of the projectile and the elevation angle h to Vbe given to the axis c of the gun barrel, the calculated time of flight Tc of the projectile being determined, by an algorithm, repetitive, but without iteration, from an estimated approximate time of ight T0 of the projectile and from the value lof said time intervals.

According to a second feature of the invention, there is provided a computer 54 which determines, from the bearing g and the site s of target A (determined by the position of the casing 23 of the rangender) and from the distance d from the target t-o the gun (supplied by the unit 53 of the rangender), the bearing G and the Vertical angle S lof the axis c of the gun barrel 31.

This computer 54 comprises:

`Coders 56, 57, S8, 59, relative to the bearing and the site of the target, which respectively deliver cos g, sin g; cos s, sin s;

A generator 60 delivering tan h, that is to say the tangent of the elevation angle h of the gun barrel, as `a function of at least the square d2 of the distance from the target to the gun;

A generator 61 delivering the value T of the time of ight of the projectile, at least as a function of the square d2 of the distance of the target from the gun;

yComputer units -62 determining, from the respective values that are delivered thereto by a central control unit 63 from memories 64 storing up the values of d, cos g, sin g; cos s, sin s and from generators 60, 61, the tangents of the calculated angular coordinates of the gun tan Gc and tan Sc, and means 65 for giving gun barrel 31 the position corresponding to the values of tan Gc and tan Se, for instance by comparing the values of tan Ge and tan Se of the gun barrel (delivered by coders 66 and 67 relative to the effective horizontal and vertical angular coordinates of barrel 31) with the calculated values of tan Gc and tan Se, through elements 68, 69 (electrovalves) which determine the angular position of the gun barrel, to reduce to zero the differences mr and n between the actual or present value and the calculated value of tan G and tan S respectively. The computer is essentially of the digital type and comprises computer units 62 which receive in the digital form the distance d of the target and the respective values delivered by the coders (cos g, sin g; cos s, sin s) and the generators (tan h, T) and deliver, also in the digital for-m, the tangents lof the bearing and the site of the gun barrel axis (tan Gc, tan Sc).

The means for controlling and aiming gun barrel 31 may advantageously comprise (FIGS. 4 and 5) two hydraulic groups 70, 71, respectively for the bearing and the site of the gun and two systems for regulating these groups.

Every hydraulic group 70-71 comprises:

A Variable output pump 72-73, driven through gears 74 from internal combustion engine 27, which drives shaft 75 with a constant number of revolutions per minute (also driving feed pump 93 through gears 92), and

A hydraulic motor 76, 77 fed, through a pipe 78, 79, with the uid (oil for instance) delivered by the corresponding pump 72, 73, this hydraulic motor acting through transmission 80 on the shaft 82 serving to control the bearing of the gun and through transmission 81 on the shaft 83 serving to control the vertical component of the angular position of the gun. Said hydraulic motor further acts upon the input shaft 84, 85 of the bearing coder 66 or of the vertical angle coder 67 respectively, which supplies, through conductors 86, 87 the successive values of tan Se and tan Ge, respectively.

The regulating system for the gun angular coordinates comprises:

A comparator 88, 89, comparator 88 receiving tan Ge and tan Gc-and-m=tan Gc-tan Ge, whereas comparator 89 receives tan Se and tan Sc and delivers n=tan Sc-tan Se,

Possibly, if the computer units 62 act upon digital values and if coders 66 and 67 deliver tan Ge and tan Se in the form of digital values, a digital-analog converter 90-91 transforming the digital value of m, n into a voltage proportional to this value and of the same sign as it,

An amplifier 94-95, amplifying the output voltage of converter 90, 91 (or of comparator 98, 99 when the output thereof is of the analog type and there is no reason to convert it) and therefore delivering a control voltage M, N representative of the difference m, n., respectively,

An electro-valve 68, 69 receiving M, N, respectively, through conductors 96, 97 and actuating, in accordance with the value of M, N, the control piston 98, 99 of pump 72, 73 to adjust the output thereof, this output depending upon M, N, and becoming zero when M, N becomes zero, and

An extrapolation loop making it possible to follow the target in a continuous manner in case of loss of sight thereof, this loop, which will be hereinafter described with reference to FIG. l1, regenerating M, N, respectively, and including for this purpose a differentiating unit 100-101 which delivers the derivative of M, N as a function of time, and a gate 102, 103, which is normally closed and is opened by the central control unit 63 when the latter ceases to be fed with correct values of the cosine and the sine of g and s respectively (a complete embodiment of such a loop will be hereinafter described with reference to FIG. ll).

Owing to this arrangement, which brings Ge to value Gc and Se to value Sc, the axis c of the gun barrel 31 is permanently kept in the direction, having angular coordinates G and S, for which a projectile fired by the gun reaches target F if the calculation of F from point A has been correctly performed (and if the target has kept moving as far as F along a path of travel TA deduced from A and from the prior positions).

Besides, there will be hereinafter described with reference to FIG. 12 a modification which comprises neither a digital-analog converter, nor analog actuating units but directly digital control actuating units.

It will now be explained, with reference to FIGS. 6 and 7, how the coordinates of the future point F are calculated in a preferred embodiment of a re control system made according to the present invention.

Calculation or prediction of the future position F, in fact of the angles G and S for pointing the gun, from continuous indications of the target bearing and site that are observed and from discontinuous indications of the distance from the target to the gun (coordinates of point A) essentially brings into play the following formulas derived from Formulas l to 8 and wherein:

A1, A2, A3 are the successive positions of A at the moments of measurement of d, to wit `O, dt, 2dt from an initial moment called zero time, where A1 is determined,

d1, d2, d3 the successive distances CA1, CA2,'CA3 at moments O, dt, 2dr

g1, g2, g3 the values of g corresponding to A1, A2,

3 obtained by sampling from the continuous measurement of g, and

s1, s2, s3 the values of Lv corresponding to A1, A2, A3 obtained by sampling from the continuous measurement of s.

In order to determine the cartesian components vx, vy, vz of the speed v of the target aircraft, present in Formulas 3 to 5 and therefore in Formulas 6, 7, 8, 1 and 2, it is necessary to make use of two sets of measurements of d, g and s taken at -a known time interval dt, the (mean) speed being equal to the ratio of the distance travelled along to the time taken to travel said distance. The iirst determination of the components of v can therefore take place only at time or moment dt, after measurement of the values of d1, g1, s1 and d2, g2, s2. If x1, y1, z1 are the cartesian coordinates of A2 atvtime dt the following relations exist.

so that the coordinates of the future point F after a time of flight T (supposed to be known) from A2, and therefore corresponding to a distance v.T travelled along by the aircraft along path of travel TA are:

The successive values of X1, Y1, Z1 are obtained by in creasing every time by two units the indexes of d, s and g. The laser rangender 60 delivers the values of d at moments or times 0, dt, 2dr therefore d1, d2, d3 whereas coders 56, 57, 58, S9, associated with this rangeiinder and with the aiming device 20 that cooperates therewith, supply (after sampling) s and g at the same moments, therefore s1, s2, s2 and g1, g2, g2 The value of dt is known: it is the period of repetition of the distance measurements by the lrangeinder and of sampling of sand g. Finally T is determined, as it will be hereinafter explained in a detailed fashion, by taking account of the firing tables which give T essentially as a function of the distance d1 of the future point F, without iteration by means of a new particular algorithm.

As a matter of fact, it is impossible to determine T directly from d1, because d1 is given by Formula 6 which contains X1, Y1, Z1 determined by Formulas 12, 13, and 14 which themselves contain T supposed to be known.

- Once X1, Y1, Z1 `are calculated, there is obtained:

On the one hand s1 or rather tan s1, given by Formula 7, so that Formula 2 gives S, or rather tan S, according to the formula tan S=tan (srl-h): (tan s-l-tan h) (l-l-tan `sf-tan h (15) which is a direct consequence of Formula 2, h being given by the :tiring tables as a function of (df)2 obtained from Formula 6,

On the other hand, gf, or rather tan gf, given by Formula 8, from which there is obtained tan G, identical to tan Gf, because G=gf (Formula l).

The determination of T will now be described with reference to FIGS. 9 and 10, FIG. 9 corresponding to the rough determination of T according to the third feature of the invention so as to supply the rough value Tb of T, whereas FIG. 10 relates to the determination of the correcting term aT to be added to Tb to take into account the duration, which is not zero, of the determination of Tb, during which the target has moved some distance and is no longer at A1, or A2, A3 for the rst, second determinations of Tb. Therefore, for instance Xf is not exactly equal to xz-l-vxb for the iirst determination of F but to (x2-l-dx) +vx.Tb, dx being the component along axis CX of the distance-dn travelled over by the target during determination of Tb.

The determination of Tb (without taking into account the correction corresponding to the duration of this determination) is performed by starting from an estimated value T0 of T. Starting from d1, s1, g1, To, d2, s2, g2, Formulas 12, 13, 14 permit of calculating the approximate values of Xf, Y2, Zr. Then Formula 6 permits of calculating an approximate value of (df)2. The firing tables supply an approximate calculated time Ts corresponding to (df)2. As a rule Ts is different from To (it would be equal to To if To were the exact value of T, or rather Tb. As a matter of fact, Ts is a function -of To and of parameters d, s and g. For predetermined average initial conditions (speed of the target, characteristics ofits path of travel) Ts is equal to f (To, d). To every value of d there corresponds a curve giving Ts as a function of To. FIG. 9 illustrates a plurality of such curves P1, P2, P3, P4 for values of d equal to 2800, 2900, 3000 and 3100 meters respectively, To being plotted in abscissas and Ts in ordinates. Straight line BS, which is the bisector of the axes of coordinates, constitutes the geometrical locus of the points for which Ts is equal to To, Vthat is to say for which T s=To=the correct value of Tb. The exact value of Tb is thereforek at the intersection of bisector BS and of the curve Ts=f(To) corresponding to the future value of the distance, therefore to df. This is why the prior methods of determining the time of ilight by iterations are long, because, as the calculation by iteration is going on, the useful curve P is moved.

The method of calculating Tb according to the third feature ofthe invention is based upon the fact that the respective measurements are made at known time intervals dt.

There is iirst taken as approximate value To obtained by dividing the distance d by a given number. In particular To may be taken, in seconds, as equal to one thousandth (or a fraction of this order) of the distance d in meters, this division by one thousand -corresponding to the normal speeds of aircrafts for the usual initial angles of site. If it is supposed, by way of example, that the value of d1 is equal to 3000, then The vertical having To as abscissa intersects curve P3 at point H, of ordinate Tso. If G1 is the point where the horizontal line passing through H intersects bisector BS, the abscissa of G1 is Tso.

The second series of determinations will take place after a time interval of 2dr. Therefore, the distance of the aircraft will be d3 corresponding to a new curve P, for instance curve P2 (unknown but looked for) in FIG. 9, such that GH (G being the intersection of horizontal line HG1 with this curve P2) is equal to 2dr. If, at this time Zdt, Tso is taken as new approximate value of T, the new value -Tsl of Ts will be the ordinate of the point E of To =3 seconds intersection of the vertical having as abscissa Tso and passing through G1 with the curve, such as P2, comprising point G. This intersection point E being not upon bisector BS, Tso` and Tsl are not identical and therefore do not represent correct values of Tb. The correct value is, on the contrary, given by the abscissa (and the ordinate) of the intersetcion K of BS with the curve P2 upon which G is located.

The approximate slope EF/F G of this curve P2 at point K is given bythe following formula The coeicieut of partition q by Tb of segment Tso, To -Zdt is given by the formula T (To-2dt)(Tsl-Ts0)+Tso(To-Tso-2dt) b Tsl-2Tso-I-To-2dt n (To2dt)Tsl-(Tso)2 (l5) Finally, Tb, that is to say the rough value of T, is calculated from:

dt, known initially,

To, taken equal to d2/ 1000 and therefore available after time di,

Tso, which can be calculated after time 2dr,

Tsl which can be used after time 4dr as hereinafter explained.

This rough value Tb must =be corrected by a value dT taking into account the movement of the target during the time of calculation 2dr of Tb, to obtain the correct value of T.

Considering FIG. -3, it is seen that it is possible to ud the values of the travel dn (and its components dx, dy, dz) of the target during time 2dr from A, as a funcf tion of the speed v of the target, of distance d and of the minimum distance dc from point C to the path of travel TA. Then, starting from dn, dI [which is a function of dn, v and d] is determined.

FIG. l0 shows the curves (straight lines) Q representing the variation of dT, as a function of d, for typical values of v and alc and for 2dt=0.1 second, the circles corresponding to the calculated points. These straight lines Q correspond to the general formula By adopting the mean values k1=0.062 and p1= 0.000027, .the error is smaller, in absolute value, than 4 milliseconds and, in relative value, than 1% Therefore, finally, one may take 0.02m dT (o.o62+ 1000 )an (16) dx=d2 cos s2 cos g2-d1 cos s1 cos g1 (18) dy=d2 cos s2 sin `g2-d1 cos s1 sin g1 dz=d2 sin s2-d1 sin s1 Finally T=Tb+dr (2o) Of course the accurate values of k1 and p1 and also that of the number by which d is divided to obtain To depend upon the type of engagement or action of the target, upon the gun and upon the projectile.

Referring now to FIG. 6, the different determinations are performed from the indications of coders 56, 57, 58, 59, which respectively deliver cos g, sin g, cos s, sin s, of coders 66, 67, which deliver the effective values of tan Ge and tan S11 and of generator means 60, 61 which deliver the time of flight T and the tangent of the elevation angle, tan h, respectively, essentially as a function of d2 (and possibly of tan S) by means of units performing the following elementary operations:

Addition, represented by the symbol -1- Subtraction, represented by the symbol Multiplication, represented by the symbol X Division, represented by the symbol Extraction of a square root, represented by the symbol For the units performing an addition or a multiplication, the two inputs are not differentiated from each other. For the substraction units the input term from which the subtraction is, effected is designated by -land the term t-o be subtracted is designated by For the division units the input corresponding to the dividend is represented by and the input corresponding to the divisor by Finally, the units of the computer illustrated by FIG. 6 also have to perform multiplication or division by a given number, for instance multiplications by p2 (unit designated by the legend xp2), divisions by 1000 (unit designated by +1000) or the addition of a constant such as k1 (unit designated by -l-k1).

Finally this computer comprises memories represented by reference letters I, I with different indexes, and switches, designated 4by reference letters U and V with different indexes, the diagram of the phases or switching times of switches U and V being illustrated by FIG. 7.

A complete cycle of prediction of the future point F comprises, as above stated, the determination of two successive values of d, g and s necessary for determining v. On the contrary, a single determination of Se and Ge is sufficient per cycle. It is therefore necessary to store up two successive values of each of the analog values of d, cos g, sin g, cos s, sin s and a single value of tan Ge and tan Se that is to say a total of twelve values. The arithmetic operations being performed on these twelve values (and those supplied by generator means 60, 61). For these twelve values a-re therefore provided twelve memories J1, 12 112 intended to store up, after two measurements (at time dt), after four measurements (at time 3dt), after six measurements (at time 5dr) the values of the following magnitudes:

da d

COS g1 COS g3 COS g5 dt Sdt 5dt sin s1 sin S5 sm s5 COS S1 COS S3 CQS S5 sin g1 5m g3 sm g5 tan S1, tan Se tan Se The twelve fixed memories 11 to 112 are fed fr-om units 53, 56, 57, 58, 59, 66, 67, through twelve intermediate memories I1 to 112, temporarily storing up the values of d, cos s, sin s, cos g, sin g, tan Se at times or moments 0i, 2dr, 4dr, and of d, cos s, sin s, cos g, sin g, tan Ge at times dt, 3dr, 5dr by means of switches U1, V1, U2, V2, V3, V4 and V5.

Switch V1 is a six positions switch which receives on every cycle successively, when its movable part rotatesA in the anticlockwise direction from the end position on the right where it is represented: d, cos s, sin s, cos g, sin g and either tan Ge or tan Se according to the position of switch U1. Switch U2 connects the output of V1 now with V2 now with V3. V2 and V2 are six positions switches rotating in synchronism with switch V1 in the clockwise direction from the end position shown by the drawing.` As for switches V4 and V5, they work in synchronism for ensuring the transfer of the contents of the twelve intermediate memories I1, I2 I11, I12 to the twelve fixed memories 11, 12, 111, 112, in fact from I1 to 11, from I2 to 12 from I11 to 111 and from 112 to 112.

Transfer of the magnitudes from the input units 53, 56, 57, 58, 59, 66, 67 to memories 11, 12, 111, 112 (FIG. 6) is performed as follows, reference being made to FIG. 7, columns I, II, III, VII, VIII and IX wherein have been shown respectively the availability of the magnitudes to the input coders 53, 56, 57, 58, 59, 66, 67 (I) to memories I1, I2, 111, I12 (II), to memories 11, 12, 111, 112 (III) and the diagrams of the phases of U1 and U2 (VII), V1, V2 and V3 (VIII) and V., and V5 (IX).

In columns I, II, and III have been symbolically inscribed the available magnitudes (in the coders, in memories I1, I2, I11, I12 and in memories 11, 12, 111, 112 respectively, as already stated), for every period O-dt, dt-Zdt, l0dt-11dt, separated into two sub-periods by the switching (of total transfer duration small with respect to dt) of the six positions switches V1, V2 and V3 indicated in the form of a horizontal pulse, same as that of the six positions switches V., and V5 (whereas the two positions switches U1 and U2 have their positions shifted at the end of every period, the duration of shifting from one position to the other, very small as compared with di, being shown by an oblique line).

The conventional signs are as follows:

An over-lined number, i.e. 'a number with a dash over it, indicates the whole of the values of d, c-os s, sin s, cos g, sin g with the index indicated by the number over which is the dash (for instance means d1, cos s1, sin s1, COS g1, Sin g1),

'S represents tan Se at the moment or time that is considered,

represents tan Ge at the moment or time that is considered, every vertical arrow indicating the period of availability of the magnitude or magnitudes inscribed opposite the upper end of the arrow.

lConsidering simultaneously FIGS. 6 arnd 7, it is seen that, at time 0, the laser rangefinder supplies the first indication of distance d1 available in the input coder 53, whereas the sighting of the rangefinder supplies, through coders 56, 57, 58, 59, the values of cos g1, sin g1, cos s1, sin s1, these five values of index 1 being represented by in FIG. 7. Finally, coders 66 and 67 deliver tan Ge and tan Se represented by and S in FIG. 7. These seven magnitudes are therefore available in the seven above mentioned coders (col. I of FIG. 7) at the beginning of period 0dt. At this zero time, switches U1 and U2 perform the switchings that have been represented: U1 corrects the output of coder 67 which it sends to V1, whereas U2 sends the output of V1 toward V2.

J7 Jg Jg Jio Jn T12 d2 cos s2 sin s2 cos g2 sin g2 tan G, d., cos s4 sm s1 cos g4 sin g4 tan G., d1 cos s1, sin s@ cos s1 sin g1 tan Ge During the -dt period, switch V1 connects its six inputs successively with its single output (see column VIII of FIG. 7). By the synchronous switching of V1 and V3 (V2 being not fed by U2) during the O-dt period, the six memories I1, I2, I2, I1, I5, I1 receive d1, cos s1, sin s1, cos g1, sin g1 and tan Se, respectively, the five first values being represented by and the last one by (see co1. II, FIG. 7, second portion of the O-dt period).

At time dt (at the end of the O-dt period) U1 performs a transfer and the sixth contact stud of V1 now receives tan G instead of tan Se. U2 also performs a transfer and now connects the output of V1 with V2 (and no longer with V3). In these conditions, the synchronous rotation of V1 and V2 during the dl-Zclt period (column VIII) sends to memories I7, I2, I9, I12, 111, I12 respectively d2, cos s2, sin s2, cos g2, sin g2 and tan Ge Iidentified by and Memories I1, I2, I11, I12 now contain, during the second portion of the dt-Zdt period, the twelve values identified by and (transferred by V2 during the 0-dt period) ,and 2 and E (transferred by V2 during the ft-2dr period), as indicated -by column II.

At the end of the dt-2dt period, at time Zdt, V4 and V5 perform,` in synchronism (col. IX), the transfer of the contents 2, E from the intermediate memories I1, 12, 111, I12 into the corresponding final memories J1, J2, 111, I12. Consequently, at the beginning of the 2dt`3dt period, memories J1, I2, J11, J12 contain 'S1-2, that is to say all the tracking and rangending quantities necessary to the computer for determining the present position and speed (at time Zdt) of the target. Subsequent values will still be necesary to determine the future point F because it is necessary -to calculate also the time of flight T, which brings other memories into play' v On the other hand, the contents of the intermediate memories I1, I2, 111, I12 having been transferred to the` final memories J1, J2, I 11, I12, memories I1, I2, t. I11, I12 are ready (after cancelling their indica 'tions throughmeans not shown on the drawing) to re- .ceive new contents. A new cycle starts for memories I1, I2, I11, I12 between times 2d! and 4dr. Memories I1 to I6 receive, durr`ing the 2dt3dt period, through switch U1 (in its left hand position), switch V1 (which cornes successively fin'tdits six positions), switch U2 (in its right hand position) and switch V2. Then memories I1 to I12 receive, during the 3dr-4d! period, E, through switch U1 (in its right hand position), switch V1 (which comes successively into l'itssix positions), switch U2 (in its left hand position) and switch V2. At the end of the 3dr-4dr period, switches V4 and V5 transfer to memories .I1 to .T12 the contents of memories I1 to I12 which are ready for a further cycle of operations.

. Therefore, it will be seen that the opertion of the system 111 of FIG. 6, which has ben described with reference to columns I, II, III, VII, VIII, IX of FIG. 7, is cyclical, ,the period of the cycle being 2d! (twice the period of relcurrence of the measurements ofthe distance of the target performed by the laser rangeiinder, because two successive distances'are necessary for calculating the speed of the target). In particular, if the rangeiinder performs 20 measurements per second, dt=0-05 s. and the cycle of system 11'1 lasts 0.1 second, every cycle being divided into two half-cycles between which switches U1 and U2 switch over.

' I will now describe the system 112 of units of FIG. 6, which permits of determining the coordinates of the future point from a duration of the time of flight T obtained, as it will be hereinafter explained, in the units 113 for calculating the rough time of light Tb, and 114, for calculating the correction dT of the time of flight.

1System 112 first comprises eight multipliers 115, 116, 117, 118, 119, 120, 121, 122 and lthree subtraction units 123, 124, 125 which determine the cartesian components vx, vy, vz of the speed v of the target.

In particular, after time 2dr, when memories J1 to .I12 contain respectively d1, cos s1, sin s1, cos g1, sin g1, tan Se, d2, cos s2, sin s2 cos g2, sin g2, tan Ge, symbolically illustrated in FIG. 7 by I, f2', (column III period 2dr-4dr), units 115 to 125 respectively deliver the following magnitudes:

System 112 also comprises three multipliers 126, 127, 128, and three adding units 129, 130, 131, deducing the cartesian coordinates X1, Y1, Z1 of the future point F from the outputs of 123, 124 and 125 and from T/dt which is supplied from a unit 132 (which will be hereinafter referred to), and this in accordance with the following formulas:

d1 cos s1 d1 sin S1, i.e. Z1

d2 cos s2 d2 sin s2, i.e. Z2

d1 cos s1 cos g1, i.e. x1

d1 cos s1 sin g1, i.e. y1

d2 cos s2 cos g2, i.e. x2

d2 cos s2 sin g2, i.e. y2

d2 cos .r2 cos g2-d1 cos s1 cos g1, i.e. vxrt d2 cos s2 sin g2-d1 cos s1 sin g1, i.e. vy.dt d2 sin s2-d1 sin S1, i.e. vZ.a't

adding units 129, 130, 131 receiving, on their two inputs, the two terms of the second member of Formulas 12 bis, 13 bis, 14 bis respectively.

System 112 further -comprises three multipliers 133.

134, 135 and two adding units 136, 137 for determining and n=tan Sc-tan Se. These units are as follows:

A divider 138 receiving, through the eight positions switches U5 and Us (only the two last positions of said switches being active), X1 and Y1 and supplying f=tan g1=tan G1, said switches beginning the switching operations at time 2dr and switching over during, and at the end of, every period di, from time 2dr (see FIG. 7, column X);

A subtraction unit or comparator 88 receiving the outputs tof 138 and I12 and delivering the difference mt=tan Gc-tan Ge which is sent, if it is in the digital form, to the digital analog comparator 90 (FIGS. 4 and 11), or, if it is in analog form, directly to amplifier 94;

A unit 139 for square root extraction which receives (X1)2{(Y1)2 from 136 and delivers tan s1= tan sf being used, on the one hand, in'combination with (alf)2 in generator means 60 and 61 (when this generator means also use tan sf) which deliver the tangent of the elevation angle, tan h, and the time of ight T as a function of (df)2 and of tan sf; generator 61 receives these two magnitudes continuously, whereas generator 60 receives them through the eight position switches U7 and U8 (only the two last Ipositions of which are active), these switches working in synchronism with switches U5 and U6 from time 2dr (see FIG. 7, column X), and, on the other hand, to determine, in the following units, tan Sc;

A multiplier 141 and an adding unit 142, each of them receiving tan s1 from 140 and tan h from 60, to calculate tan sf tan h and tan sf-l-tan h, respectively;

An adding device 143 adding one unit to the output of 141 so as to deliver 1-i-tan s1 tan h and a divider dividing the output 142 by the output of 143 so as to deliver.

tan sf-I-tan h ta SW1-Han sfxtan h Finally a subtraction or comparator unit 89 receiving the outputs of 144 and of 16 and delivering the difference nztan Sc-tan Se, which is transmitted, if it is in digital form, to the digital-analog converter 91 (FIG. 4), or, if it is already in analog form, directly to amplifier 95.

It is necessary now to explain with what units and how the computer of FIG. 6 determines the correct value `of the time of flight T by the algorithms above indicated with reference to FIG. 9 (determination of the rough value Tb of T) and to FIG. l (determination of the correction term dT to be added to Tb for giving T).

Concerning first the calculation of the rough value Tb, it is determined by system 113- which comprises:

An eight positions Switch U4 (two interconnected active positions, two interconnected active lpositions, two interconnected active positions, two inactive positions) rotating like switches U to U8 during, and at the end of, every dt period, from time 2dt;

A device for dividing by 1000, designated by 145, which receives the output of memory 17, to wit d2 at time 2dt, and which delivers To, which is therefore available from time Zdt (see FIG. 7, column IV, wherein arrows indicate the availability of the determined magnitudes-whereas columns I, II and III represent the availability of the input magnitudes-the magnitudes in question being indicated at the level of the upper ends of the arrows). The output of 145, to wit To, is sent to the two first studs of switch U4. Consequently, during period 2dr-3dr, U4 transmits To to 132 which delivers To/dt to -multipliers 126, 127, 128. Units 126, 127, 128, 129, 130, 131, 133, 134, 135, 136 and 137 determine an approximate value of (d1)2 (based upon To) which reaches the time of flight generator 61 at the same time as an approximate value of tan sf (also based upon To) calculated by units 139 and 140 from the outputs of 135 and 137. Generator 61 then delivers the approximate value Tso, which is the ordinate of point H (FIG. 9) the abscissa of which is To, this value Tso being used for the calculation of the rough value of T by Formula 15, whereas, on the contrary, the generator 60 of tan h, units 141, 142, 143, 144 for calculating tan Sc and unit 1318 for calculating tan Gc are not fed with current (the movable part of switches U7, U8, U5, U6 being on an unconnected stud), because the approximate values of tan h, tan Sc and tan Gc are not used in this embodiment of the invention (it will be seen that, on the contrary, in the embodiment of FIG. 13 the angles Sc and Gc deduced from To are imparted to the gun barrel);

A memory 113 intended to store up Tso;

A switch U3 analogous to switches U4 to U8 and rotating in synchronism therewith (FIG. 7, column X), but the output studs of which are connected differently so that in positions 2, 3 and 4, when it receives Tso` from 16 61, it delivers it to memory 113 which thus receives Said value Tso which it stores up and which it transmits, when switch U4 occupies positions 3 and 4 (period 3dt4dt), to unit 132, which corresponds to the determination of new approximate values of 11)2 and tan sf from 2, this determination being now based upon Tso. The time of flight generator 61 receives these new approximate values and operates at point E (FIG. 9) to deliver TS1 to switch U3 which now comes into its last four positions wherein it transmits Ts1 through conductor 146. As above, switches U5, U6, U7, U8 do not feed current, the determinations of tan Sc and tan Gc being based upon an approximate value of TS1, and

A subassembly for determining the rough value of T from To, Tso, TS1 (and dt) according to Formula 15.

This subassembly comprises:

A subtraction unit 148, which subtracts Zdt (constant equal for instance to 0.1 second) from the output of and therefore delivers To-Zdt (abscissa of point G in FIG. 9);

Two multiplication units 149 and an addition unit 150 both receiving T s1 from U3 through 146 and To-Zdt from 148;

Two multipliers 151, 152, multiplier 151 receiving Tso (from 113) on both of its inputs and therefore delivering (Ts0)2, whereas multiplier 152 receives, on its single input, TSO (from 113) and multiplies this magnitude by two so as to` deliver 2Tso;

Two subtraction units 153, 154, the first one subtracting the output of 151 from that of 149 and the second subtracting the output of 152 from that of 150; and

A divider 155 dividing the output of 153, to wit (To-2dt)Ts1-(Ts0)2, by the output of 154, to wit Tsl-1-(T0-2dt)-2Tso, so as to deliver the rough value Tb of T (identical coordinates of the point K of FIG. 9), to wit This rough value Tb must be corrected with value aT corresponding to the time interval, which is not equal to zero but to 2dr, for calculating Tb starting moment or time 2dt.

For this purpose, the computer illustrated by FIG. 6 comprises system 114 which includes:

Three multipliers 156, 157, 15S each of which delivers the square of the magnitude it receives on both of its inputs, this magnitude being, respectively, dx received from 123 and supplied to 156, dy received from 124 and supplied to 157 and dz received from 125 and supplied to 158;

An adding unit 159 which receives (dx)2, (dy)2, (dz)2 from 156, 157, 158 respectively and delivers A unit 160 extracting the square root of the magnitude applied to its input, which receives (dn)2 from 159 and therefore delivers dn at its output;

A divider by 100, designated by reference numeral 161, receiving dn from 160 and delivering dn/ 100;

A multiplier 162 multiplying its input by and an adding device 163, adding k1=0.062, disposed in series, unit 162 receiving To (that is to say d/ 1000) and therefore delivering 0.000027 d to 163, which therefore delivers 0.062-|0.'000027 d, i.e. k1|p1d, and

A multiplier 164 receiving the outputs of 161 and 163 and therefore delivering v This time of ight corrective term dT is added to the rough time of flight Tb in an adding unit 165 which receives the outputs of 164 (dT) and of 155 (Tb) and therefore delivers the correct value T of the time of flight to a memory 114 which feeds the studs 5 and 6 of switch U4. The latter therefore delivers T during the period from 4dr to Sdt, the value of T being then available at the output of U4. Units 126, 127 and 128 then receive the exact value of T and can undergo, together with units 129, 130, 131, the calculation of the exact values of the cartesian coordinataes Xt, Yf, Z, of the future point F, which are determined at the beginning of the 5dr-6dr period (FIG. 7, column V, which gives the values obtained from the values located at the same level in column VI) from this value of T and from S, E. The correct values of Xf, Yf, (df)2, tan sf `are then available at the outputs of units 129, 130, 13-7 and 140 respectively, and switches U5, Us, U7, U8 which are then on their two last studs (the only ones to be active in the embodiment of FIG. 6), deliver these correct values to units 60 and 138 which therefore deliver the correct values of tan h and tan gf=tan Gc. Unit 144 then delivers the correct value of tan Sc. Finally, 88 and 89 deliver the correct values of m and n.

The first complete cycle SG1 which permits of determining m and n, has therefore lasted 6dt and is therefore finished at time 6dt. At this time, another complete cycle SC2 starts. It vwill be noted that the second complete cycle SC2 and the following cycles have only a duration of 4dr, because the preliminary period PP between times and 2dr is no longer necessary, since magnitudes '5, S, 6, 'G are already available at time 6dr. FIG. 7 thus illustrates between times 0 and l0dt, the two rst complete cycles (for the sake of simplicity this figure does not show the contents of columns and 6 after the time 7dr).

Thus it will be seen that the computer of FIG. 6 permits of calculating, with a rate of repetition of 4dr, thatv is to say 0.2 second if dt is equal 0.05 second, tan Gc and tan Sc which determine the values of the firing coordinates of the gun barrel. These values are compared, in compara-4 tors 88 and 89, to tan Ge and Se determined by the effective coordinates of the gun barrel, the differences m=tan Gc-tan Ge and n=tan .Sc-tan Se representing the difference to be corrected by the control means described with reference to FIGS. 4 and 5.

The above calculation requires knowing g and s substantially in a continuous manner (in particular at the times of sampling by V1). If the target (aircraft) passes through clouds and is no longer visible through telescope 20, only sin g, cos g, sin s, cos s are available in memories J1. to J 12 (whereas .the laser ranigefinder 16 might, in some cases keep supplying the values of d) and the calculation of tan G and tan S is no longer possible. Y g

This is why, in order to ensure t'he continuity of firing, an extrapolation device (already referred to with reference to FIG. 4) is provided foreach magnitude G and S or m and n. An embodiment of such an extrapolation device has been illustrated by FIG. 11, which shows ian extrapolation device for tan Gc or m, the extrapolation f device for tan Sc or n being similar.

The magnitude m=tan Gc-tan Ge, normally delivered by comparator 88, is preliminarily transformed into analog magnitude in the case where it is digital when the extrapolation device is, las illustrated by FIG. l1, of the analog type (in the improved embodiment of FIG. l2 the apparatus is entirely of the digital type). A digitalanalog converter 90 of a known type is used for this transformation. I'he output voltage of converter 90 (which represents, in the case of a normal following, the difference between the tangent of the effective bearing of the gun barrel and the tangent of the bearing that should be ygiven to this barrel for reaching the target at future point F) passes through a normally open gate 166 the output of which is connected to a first input 94a of amplifier 94, which delivers the amplified control voltage M for the electro-valve 68 of the piston 98 of the hydraulic pump 72 (FIGS. 4 and 5). A differentiator 100 of a known 18 type, including a resistor 167 and a capacitor 168, dcduces the derivative dM/dt of M. This derivative is fed in an impedance matcher 169 before being applied to a normally closed gate 102, the output of which is connected to a second input 94b of amplifier 94.

In case of normal optical tracking of the target by means of telescope 20, :amplifier 94 -therefore amplies theoutput of 90, gate 166 being open whereas gate 102 is closed (it is the first input 94a of amplifier 94 which is fed with current). On the contrary, when the target aircraft is lost of view through telescope 20, the gunner or the central control unit 63 sends an order 00 for the continuation of tracking, which is decomposed into two orders to wit :a blocking order 01 and an unblocking order 02 (deduced from 00 by conversion in a NON or inverter circuit 170). From this time on, gate 166 is closed whereas gate 102 is open :and it is the second input 94b of amplifier 94 which is fed with the derivative dM/ dt. Therefore the output of amplifier 94 keeps moving the gun barrel in accordance with the preceding law of displacement. With the possible exception of the determination of the derivative of mand n (inthe case'of extrapolation devicesof the type illustrated by FIG. 11), the operations are very advantageously carried out in the digital form in the system according to the present invention and it is such a digital embodiment of the computer of FIG. 6 according to the process illustrated by FIG. 7 which will now be described with reference to FIG. 8. However it should be noted that it is possible, if so desired, to apply some features -of the invention in an analog form or in.a mixed or hybrid form (partly analog and partly digital), the different units of FIG. 6 (adding units, multipliers, dividers, subtraction units, square root extraction units) being then constituted by analog units of known type, for instance of one of the types described in the book of Walter W. Soroka Analog Methods in Computation and Simulation (McGraw-Hill Books Company Inc. 1954). On the contrary the present description will relate to a preferred embodiment of a digital computer.

The digital electronic computer which will be herein- 'after described with reference to FIG. 8 performs substantially the same operations as those above described with reference to FIGS. 6 and 7. However, whereas, in an analog computer, every unit of FIG. 6 truly exists, in a digital computer, the number of units is reduced, since the same unit, for instance the same multiplying unit, successively performs the same multiplication operation on different numbers. It is the program of instructions which determines the succession of operations 'and the input aud/ or calculated numbers on which the operations must be performed in every unit.

Here is the sequence flow sheet of the operations to be performed by the digital computer summing up the program of detailed instructions, attention being called to the two following points:

( 1) It is necessary to perform, as above stated, three successive determinations of the coordinates of the future point, to wit:

Starting from To 'and from the first pair of coordinates S, 2`, E, Tm is determined by the time of flight generator means,

Starting from Tso and from the next pair of coordinates S, TS1, then Tb is determined by Formula 15, and T is determined by adding aT to Tb,

Starting from T and the third pair of coordinates S, E, the correct values of Xf, Yf, Zf are obtained.

The sequence flow sheet must therefore comprise three v successive cycles of calculation corresponding to the three successive active position of U4 (FIG. 6). To this effect, there is introduced in the data a quantity, called L, which assumes, during the computing cycles, successively three values, such as -E, 0, +B, the change of value taking place on every determination of the time of fiight by addition of -l-E to the actual value of L (the initial value of L being -E). The machine performs,

according to the values of L at the beginning of the determination of the time of flight the operations corresponding to the determination of Tso, of Tsi, of Tb (then 0f T). Thus, taking for instance initially L as equal to -l and adding a unit to L during every cycle of determination of the time of Hight, that is to say E being taken equal to 1, the machine first compares L to 0. If L is smaller than 0 (which is the case of the first determination cycle), the machine proceeds in determining Tso and adding E (equal to 1) to L, so that L shifts from -1 to 0. On the contrary, if L is positive or equal to zero, the machine checks up the logical equivalence of L and E that is to say 1. In the particular example, in case of non equivalence (which is the case for the second cycle when E is equal to 0), the machine performs the determination of TS1 and the addition of E (equals to 1) to L, so that L shifts from zero to +1, whereas in case of logical equivalence, which is the case for the third cycle because L has become equal to E: 1, the machine determines Tb.

(2) Extraction of the square roots by the digital computer is performed by `starting from an approximate value p, of the square root. p1 is chosen for instance equal to 20 for the determination of \/(dn)2 (it being supposed that the target moves a distance of 20 meters during the time interval 2d!) and equal to the greater of the numbers Xf, Yf, for the determination of \/(Xf)2+(Yf)2,

20 because this last mentioned square root is comprised between the greater of these numbers (in the case where the other would be equal to zero) and the product thereof by V (in the case where both numbers would be equal to each other). The machine performs the division of number ni, the square root of which is to be extracted, by the approximate value p, and therefore determines the quotient Then it compares q1 to p1 and if the difference in absolute value lq-pl] is greater than a very small given quantity e, it repeats the operation, taking as new approximate value of the square root 1/2(pi|q1), which becomes the new pi. When, finally, there is obtained a value of pi such that [q1-pil is smaller than e, the corresponding quotient is the value of the square root of n1.

These two preliminarily explanations being given, here is an example of a sequence ilow sheet for the digital computer.

t=0 4dt d1 tan Se cos s1 cos g1 sin s1 sin g1 t1=dt da tan Ge cos sz cos g2 sin sg sin g2 t2=2dt da tan Se cos sa cos gs sin s3 sin g3 ta=3dt d4 tsm Gs cos s4 cos a4 sin s4 sin g4 Introduction of the data Tn-dq/lOOO k To/dt from determination ofthe time of flight for the future position Start at t=2 dt Zf= d1 Sin the coordinates of the future position means for generating functions f1 dz2= (da cos s, c os (1r-d1 cos 81 cos 002 dy2=(dr cps sg sm ga-di cos si sin g1)z 122: (dg sin .s3-d1 sin s1)2 Determination of the correcting term for qi=dnlpi extraction 0I the the time oi ight .l square root of cm2 toward determination |qa-pal1e of the time of ight ior thc future position dt=o 062+@ (mix-'"- from determination of the correcting term for the time of ght 1.0 I logical determination of equivalence E the time of ight for the future position N0 Tb Ta Tb TS1 T dt k mm T wo-21u) 1x1-(Twp b" T12T+T 2a:

L+E L(= 0) T= Th-I-dT Wait until 4dt; indexes, 2,1 become 4,3 T/dt k toward determination of the coordinates ofthe future position m L+E L(=ji1) 7lo2'-`(Xf)2|-(Yf)2 I XfzYx extraction of the square root of (no)z X1 Ti Y: Y; 1-4 Determination o! the I. AI

firing coordinates m=tan Gc-tan Ga extract m, 'n

Start again In order to carry out such a sequence iiow sheet the computer must therefore essentially perform the following operations:

Addition; subtraction; multiplication;

The limitation of 13 bits makes it necessary to limit the maximum values of angle Ge and Se and also the amplitude of the output signals m, n.

In addition to the 13 bits for the mantissa of the numdivision In the arithmetic bers, it iS IleCeSSary t0 provide 6 bits for the exponent units, (ranging from 0 to 16) and one bit for the sign that is Transfer; normal jump From one register t0 Say a tOtal 0f 20 bits for the magnitudes.

to another. 40 This may be summed up in the following table: Conditional jump If a condition is fulfilled. Sign Exponent Mantissa Logical equivalence; logical non-equivalence; direct shifting; generation of From 11 to 14-.--- From so to 999. functions f1 and f2. tratara-:f armata. that is to say 11 operations. Frome to 11-....- From o to 999.

Advantageously these operations are performed in a machine of the type illustrated by FIG. 8, bringing into play a method of series calculation in the pure binary code, with a. variable position comma.

With a binary code, the input and the output signals may be defined as follows, by limiting the mantissas of the numbers to 13 binary orders or bits that is to say to 4096 distinct discrete values:

The computer processes the exponents and the mantissas separately.

As for the instructions, they are of the type with two addresses, to wit that of the register or memory from which the machine must extract the number to be processed and that of the register or memory to which the result is to be transferred, and they further comprise the Detni- Limit of the Magnitude Coming from Limit of the true values tion values in the computer d Laser range-finder 16 From 400 m to 4,500 m. 5 m. From 80 to 900.

cos s, cos g, sin s, sin g. Coders 56, 57 ,58, 59...--.- From Oto 0.999 0.001.... From 0 to 999.

tanG... tan Se Coders 66, 67 From Oto 4.096 (Gs and 0.001.... From Oto 4096.

Se ranging from 0 to 785).

tan h Angle of elevation From 0 to 0.053 (h ranging 0.001. From 0 to 53.

Y generator means 60. from 0 to 3).

T Time of flight generator From 0 to 4.995 s 0.005 s... From 0 to 999.

means 61.

dt Laser range-finder 16 0.05 s 0.005 s.-. 10.

m, n Output signals From 0 to 4.096 0.001.... From Oto 4096. 

1. A FIRE CONTROL SYSTEM FOR DIRECTING A GUN TOWARD A TARGET WHICH COMPRISES, IN COMBINATION, MEANS FOR DETERMINING SUBSTANTIALLY IN A CONTINUOUS MANNER THE ANGULAR COORDINATES OF SAID TARGET, MEANS FOR DETERMINING THE DISTANCE OF THE TARGET FROM THE GUN AT REGULAR TIME INTERVALS. AND MEANS FOR CALCULATING THE ANGULAR COORDINATES TO BE GIVEN TO SAID GUNS, SO THAT A PROJECTILE FIRED THEREFROM NORMALLY REACHES SAID TAGRET, FROM SAID ANGULAR COORDINATES OF THE TARGET, THE DISTANCE OF THE TARGET FROM THE GUN,THE DURATION OF SAID TIME INTERVALS AND THE INDICATIONS OF FIRING TABLES GIVING, FOR SAID DISTANCE, THE TIME OF FLIGHT OF THE PROJECTILE AND THE ELEVATION ANGLE TO BE GIVEN TO THE GUN, THE CALCULATED TIME OF FLIGHT OF THE PROJECTILE BEING DETERMINED, BY AN ALGORITHM, REPETITIVE, BUT WITHOUT ITERATION, FROM AN ESTIMATED APPROXIMATE TIME OF FLIGHT OF THE PROJECTILE AND FROM THE DURATION OF SAID TIME INTERVALS. 